Which of these numbers is prime? ${9,\ 55,\ 77,\ 84,\ 97}$
Solution: A prime number has exactly two factors: 1 and itself. The factors of 9 are 1, 3, and 9. The factors of 55 are 1, 5, 11, and 55. The factors of 77 are 1, 7, 11, and 77. The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. The factors of 97 are 1 and 97. Thus, 97 is a prime number.